Because of the delocalized bonding in graphite, graphite is able to conduct electricity. I'd figure benzene, which has a similar structure, would be able to conduct electricity. Is this so?

No, it is not.

In graphite, the [itex]\pi[/itex]-electrons are delocalized over the entire plane of C-atoms, while in a benzene molecule they are only delocalized within the molecule (ring). There is no mechanism in benzene to allow the electrons to hop from one molecule to another. This is similar to the fact that in-plane delocalization in graphite means you can conduct well only along a single plane but not from one plane to the next.